Finding the unit of θ in ΔT = Pθ using dimensional analysis

[fran1942]

Homework Statement

In the equation ΔT = Pθ, P is power in Joules per second and ΔT is the temperature difference in °C. Use dimensional analysis to find the unit of θ. Hint, Joules has units of Force time distance.

My question is: I don't understand what they mean by finding the unit of θ. Are they saying that P needs to be multiplied by θ, or does θ simply represent the unit of P that I have worked out below ?
Sorry, I am unfamiliar with how Physics questions are worded.

The Attempt at a Solution

I am pretty sure the answer is m^2 kg / s^3
If correct, how does my answer relate to θ ?

 

[edgepflow]

This expression is the first law of thermo. See if you can find an equation for theta based on physical constants and variables and I think it will make sense.

 

[fran1942]

thanks, so is my answer of m^2 kg / s^3 not correct ?